紧支撑半正交小波的构造  

On the Construction of Compactly Supported Prewavelets

作　　者：李云章[1] 刘慧敏[1] 

机构地区：[1]北京工业大学应用数学系,北京100022

出　　处：《洛阳大学学报》2007年第2期1-8,共8页Journal of Luoyang University

基　　金：国家自然科学基金资助项目(项目编号:10671008);北京市优秀人才基金资助项目(项目编号:20051D0501022);北京市中青年骨干教师基金;教育部留学回国人员科研启动基金资助项目

摘　　要：众所周知,一个紧支撑细分函数若生成一个正交的多分辨分析(MRA),则该MRA可容许一个具有紧支撑的小波,并且小波有明确的表达式.但若生成一个非正交的多分辨分析,我们却没有一个构造紧支撑半正交小波的一般方法.Chui与Wang曾在尺度函数紧支对称的前提下,给出了一个构造紧支撑半正交小波的方法,给出了紧支撑半正交样条小波的构造例子.但这种方法依赖于一个多项式零点的确定,在大多数情况下这是不很容易的.本文在适当的条件下,给出了一个构造半正交小波的方法.这种构造继承了来源于尺度函数和符号的对称性和消失矩性质.我们也给出了两个例子来说明这种方法.It is well known that, if a compactly supported refinable function generates an orthogonal MRA, then the basic wavelet can be explicitly constructed and compactly supported. But interestingly if it generates a nonorthogonal MRA, there has not been a general recipe to construct a compactly supported basic prewavelet. Chui and Wang obtained an approach to construct a compactly supported basic prewavelet under the hypothesis that the scaling function is symmetric. Unfortunately, the approach by Chui and Wang highly depends on the determination of zeros of a polynomial, which is difficult in most cases. Using many properties of spline functions, Chui and Wang also constructed compactly supported spline prewavelets. In this paper, a construction of basic prewavelet is obtained under a mild hypothesis. What is more, this construction inherits the symmetry and vanishing moment originating in general theory. scaling functions and symbols. Two examples are also given to illustrate the general theory.

关 键 词：尺度函数 半正交小波 RIESZ基 

分 类 号：O174.2[理学—数学] O174.3[理学—基础数学]